2. **Endothermic reactions. As discussed in lecture, Eq. (14.53) of Taylor assumes elastic scattering. If energy is lost (or gained) in a collision, the factor \ in Eq. (14.53) is replaced by m1 Q -1/2 m1 = 1+ m2 To m2. (4) where Q is the energy lost in the reaction. Also, the final center-of-mass velocity of particle 1 is viem = m2V1lab m1 + m2 Q a (1+ M1 To M2 (5) (a) Consider an endothermic reaction between two particles of equal mass. In the lab frame, particle 1 initially has kinetic energy To and particle 2 is initially at rest. Compared to To, how much kinetic energy does particle 1 have initially in the center-of-mass frame? (b) Compared to To, how much combined kinetic energy do particle 1 and parti- cle 2 have initially in the center-of-mass frame? (c) For what value of Q/To do the particles have zero velocity in the center-of- mass frame following the collision? (d) Explain (i) physically and (ii) mathematically why the reaction cannot occur if Q/To is greater than the threshold value you found in part (c). (e) Draw four diagrams that show the initial and final velocities in the laboratory and center-of-mass frames for the threshold value of Q/To that you found in part (c). (f) What is the total cross section of this reaction when To is smaller than the threshold you found in part (c)?